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1.
Stochastic analysis is commonly used to address uncertainty in the modeling of flow and transport in porous media. In the stochastic approach, the properties of porous media are treated as random functions with statistics obtained from field measurements. Several studies indicate that hydrological properties depend on the scale of measurements or support scales, but most stochastic analysis does not address the effects of support scale on stochastic predictions of subsurface processes. In this work we propose a new approach to study the scale dependence of stochastic predictions. We present a stochastic analysis of immiscible fluid–fluid displacement in randomly heterogeneous porous media. While existing solutions are applicable only to systems in which the viscosity of one phase is negligible compare with the viscosity of the other (water–air systems for example), our solutions can be applied to the immiscible displacement of fluids having arbitrarily viscosities such as NAPL–water and water–oil. Treating intrinsic permeability as a random field with statistics dependant on the permeability support scale (scale of measurements) we obtained, for one-dimensional systems, analytical solutions for the first moments characterizing unbiased predictions (estimates) of system variables, such as the pressure and fluid–fluid interface position, and we also obtained second moments, which characterize the uncertainties associated with such predictions. Next we obtained empirically scale dependent exponential correlation function of the intrinsic permeability that allowed us to study solutions of stochastic equations as a function of the support scale. We found that the first and second moments converge to asymptotic values as the support scale decreases. In our examples, the statistical moments reached asymptotic values for support scale that were approximately 1/10000 of the flow domain size. We show that analytical moment solutions compare well with the results of Monte Carlo simulations for moderately heterogeneous porous media, and that they can be used to study the effects of heterogeneity on the dynamics and stability of immiscible flow. 相似文献
2.
J. T. Shiau 《Stochastic Environmental Research and Risk Assessment (SERRA)》2003,17(1-2):42-57
Extreme hydrological events are inevitable and stochastic in nature. Characterized by multiple properties, the multivariate
distribution is a better approach to represent this complex phenomenon than the univariate frequency analysis. However, it
requires considerably more data and more sophisticated mathematical analysis. Therefore, a bivariate distribution is the most
common method for modeling these extreme events. The return periods for a bivariate distribution can be defined using either
separate single random variables or two joint random variables. In the latter case, the return periods can be defined using
one random variable equaling or exceeding a certain magnitude and/or another random variable equaling or exceeding another
magnitude or the conditional return periods of one random variable given another random variable equaling or exceeding a certain
magnitude. In this study, the bivariate extreme value distribution with the Gumbel marginal distributions is used to model
extreme flood events characterized by flood volume and flood peak. The proposed methodology is applied to the recorded daily
streamflow from Ichu of the Pachang River located in Southern Taiwan. The results show a good agreement between the theoretical
models and observed flood data.
The author wishes to thank the two anonymous reviewers for their constructive comments that improving the quality of this
work. 相似文献
3.
Copula-based geostatistical modeling of continuous and discrete data including covariates 总被引：4，自引：3，他引：1
Hannes Kazianka Jürgen Pilz 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(5):661-673
It is common in geostatistics to use the variogram to describe the spatial dependence structure and to use kriging as the spatial prediction methodology. Both methods are sensitive to outlying observations and are strongly influenced by the marginal distribution of the underlying random field. Hence, they lead to unreliable results when applied to extreme value or multimodal data. As an alternative to traditional spatial modeling and interpolation we consider the use of copula functions. This paper extends existing copula-based geostatistical models. We show how location dependent covariates e.g. a spatial trend can be accounted for in spatial copula models. Furthermore, we introduce geostatistical copula-based models that are able to deal with random fields having discrete marginal distributions. We propose three different copula-based spatial interpolation methods. By exploiting the relationship between bivariate copulas and indicator covariances, we present indicator kriging and disjunctive kriging. As a second method we present simple kriging of the rank-transformed data. The third method is a plug-in prediction and generalizes the frequently applied trans-Gaussian kriging. Finally, we report on the results obtained for the so-called Helicopter data set which contains extreme radioactivity measurements. 相似文献
4.
Ke-Sheng Cheng Ju-Chen Hou Jun-Jih Liou Yii-Chen Wu Jie-Lun Chiang 《Stochastic Environmental Research and Risk Assessment (SERRA)》2011,25(2):107-122
A frequency-factor based approach for stochastic simulation of bivariate gamma distribution is proposed. The approach involves
generation of bivariate normal samples with a correlation coefficient consistent with the correlation coefficient of the corresponding
bivariate gamma samples. Then the bivariate normal samples are transformed to bivariate gamma samples using the well-known
general equation of hydrological frequency analysis. We demonstrate that the proposed bivariate gamma simulation approach
is capable of generating random sample pairs which not only have the desired marginal densities of component random variables
but also their correlation coefficient. Scatter plots of simulated bivariate sample pairs also exhibit appropriate linear
patterns (dependence structure) that are commonly observed in environmental and hydrological applications. Caution should
also be exercised when specifying combinations of coefficients of skewness and the correlation coefficient for bivariate gamma
simulation. 相似文献
5.
The authors present a statistical procedure to estimate the probability distributions of storm characteristics. The approach uses recent advances in stochastic hydrological modeling. The temporal dynamics of rainfall are modeled via a reward alternating renewal process that describes wet and dry phases of storms. In particular, the wet phase is modeled as a rectangular pulse process with dependent random duration and intensity; the global dependence structure is described using multidimensional copulas. The marginal distributions are described by Generalized Pareto laws. The authors derive both the storm volume statistics and the rainfall volume distribution within a fixed temporal window preceding a storm. Based on these results, they calculate the antecedent moisture conditions. The paper includes a thorough discussion of the validity of the assumptions and approximations introduced, and an application to actual rainfall data. The models presented here have important implications for improved design procedures of water resources and hydrologic systems. 相似文献
6.
《Geofísica Internacional》2014,53(2):163-181
This paper introduces a general nonparametric method for joint stochastic simulation of petrophysical properties using the Bernstein copula. This method consists basically in generating stochastic simulations of a given petrophysical property (primary variable) modeling the underlying empirical dependence with other petrophysical properties (secondary variables) while reproducing the spatial dependence of the first one.This multivariate approach provides a very flexible tool to model the complex dependence relationships of petrophysical properties. It has several advantages over other traditional methods, since it is not restricted to the case of linear dependence among variables, it does not require the assumption of normality and/or existence of moments.In this paper this method is applied to simulate rock permeability using Vugular Porosity and Shear Wave Velocity (S-Waves) as covariates in a carbonate double-porosity formation at well log scale. Simulated permeability values show a high degree of accuracy compared to the actual values. 相似文献
7.
The continuous time random walk (CTRW) has both an elegant mathematical theory and a successful record at modeling solute transport in the subsurface. However, there are some interpretation ambiguities relating to the relationship between the discrete CTRW transition distributions and the underlying continuous movement of solute that have not been addressed in existing literature. These include the exact definition of “transition”, and the extent to which transition probability distributions are unique/quantifiable from data. Here, we present some theoretical results which address these uncertainties in systems with an advective bias. Simultaneously, we present an alternative, reduced parameter CTRW formulation for general advective transport in heterogeneous porous media, which models early- and late-time transport by use of random transition times between sparse, imaginary planes normal to flow. We show that even in the context of this reduced-parameter formulation there is nonuniqueness in the definitions of both transition lengths and waiting time distributions, and that neither may be uniquely determined from experimental data. For practical use of this formulation, we suggest Pareto transition time distributions, leading to a two-degree-of-freedom modeling approach. We then demonstrate the power of this approach in fitting two sets of existing experimental data. While the primary focus is the presentation of new results, the discussion is designed to be pedagogical and to provide a good entry point into practical modeling of solute transport with the CTRW. 相似文献
8.
Bivariate frequency analysis of nonstationary low‐flow series based on the time‐varying copula 
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下载免费PDF全文 Many studies have analysed the nonstationarity in single hydrological variables due to changing environments. Yet, few researches have been done to investigate how the dependence structure between different individual hydrological variables is affected by changing environments. To investigate how the reservoirs have altered the dependence structure between river flows at different locations on the Hanjiang River, a time‐varying copula model, which takes the nonstationarity in the marginal distribution and/or the time variation in dependence structure between different hydrological series into consideration, is presented in this paper to perform a bivariate frequency analysis for the low‐flow series from two neighbouring hydrological gauges. The time‐varying moments model with either time or reservoir index as explanatory variables is applied to build the time‐varying marginal distributions of the two low‐flow series. It's found that both marginal distributions are nonstationary, and the reservoir index yields better performance than the time index in describing the nonstationarities in the marginal distributions. Then, the copula with the dependence parameter expressed as a function of either time or reservoir index is applied to model the variable dependence between the two low‐flow series. The copula with reservoir index as the explanatory variable of the dependence parameter has a better fitting performance than the copula with the constant or the time‐trend dependence parameter. Finally, the effect of the time variation in the joint distribution on three different types of joint return periods (i.e. AND, OR and Kendall) of low flows at two neighbouring hydrological gauges is presented. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
9.
Permissibility of fractal exponents and models of band-limited two-point functions for fGn and fBm random fields 总被引：1，自引：1，他引：0
The fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) random field models have many applications in the environmental sciences. An issue of practical interest is the permissible range and the relations between different fractal exponents used to characterize these processes. Here we derive the bounds of the covariance exponent for fGn and the Hurst exponent for fBm based on the permissibility theorem by Bochner. We exploit the theoretical constraints on the spectral density to construct explicit two-point (covariance and structure) functions that are band-limited fractals with smooth cutoffs. Such functions are useful for modeling a gradual cutoff of power-law correlations. We also point out certain peculiarities of the relations between fractal exponents imposed by the mathematical bounds. Reliable estimation of the correlation and Hurst exponents typically requires measurements over a large range of scales (more than 3 orders of magnitude). For isotropic fractals and partially isotropic self-affine processes the dimensionality curse is partially lifted by estimating the exponent from measurements along fixed directions. We derive relations between the fractal exponents and the one-dimensional spectral density exponents, and we illustrate the relations using measurements of paper roughness.The author would like to acknowledge helpful comments from two anonymous referees. 相似文献
10.
11.
The coherence method is always used to describe the discontinuity and heterogeneity of seismic data. In traditional coherence methods, a linear correlation coefficient is always used to measure the relationship between two random variables (i.e., between two seismic traces). However, mathematically speaking, a linear correlation coefficient cannot be applied to describe nonlinear relationships between variables. In order to overcome this limitation of liner correlation coefficient. We proposed an improved concordance measurement algorithm based on Kendall’s tau. That mainly concern the sensitivity of the liner correlation coefficient and concordance measurements on the waveform. Using two designed numerical models tests sensitivity of waveform similarity affected by these two factors. The analysis of both the numerical model results and real seismic data processing suggest that the proposed method, combining information divergence measurement, can not only precisely characterize the variations of waveform and the heterogeneity of an underground geological body, but also does so with high resolution. In addition, we verified its effectiveness by the actual application of real seismic data from the north of China. 相似文献
12.
13.
For decades, stochastic modellers have used computerized random number generators to produce random numeric sequences fitting a specified statistical distribution. Unfortunately, none of the random number generators we tested satisfactorily produced the target distribution. The result is generated distributions whose mean even diverges from the mean used to generate them, regardless of the length of run. Non‐uniform distributions from short sequences of random numbers are a major problem in stochastic climate generation, because truly uniform distributions are required to produce the intended climate parameter distributions. In order to ensure generation of a representative climate with the stochastic weather generator CLIGEN within a 30‐year run, we tested the climate output resulting from various random number generators. The resulting distributions of climate parameters showed significant departures from the target distributions in all cases. We traced this failure back to the uniform random number generators themselves. This paper proposes a quality control approach to select only those numbers that conform to the expected distribution being retained for subsequent use. The approach is based on goodness‐of‐fit analysis applied to the random numbers generated. Normally distributed deviates are further tested with confidence interval tests on their means and standard deviations. The positive effect of the new approach on the climate characteristics generated and the subsequent deterministic process‐based hydrology and soil erosion modelling are illustrated for four climatologically diverse sites. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
14.
Etienne Mémin 《地球物理与天体物理流体动力学》2014,108(2):119-146
We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition is reminiscent in spirit to the classical Reynolds decomposition. However, the random velocity fluctuations considered here are not differentiable with respect to time, and they must be handled through stochastic calculus. The dynamics associated with the differentiable drift component is derived from a stochastic version of the Reynolds transport theorem. It includes in its general form an uncertainty dependent subgrid bulk formula that cannot be immediately related to the usual Boussinesq eddy viscosity assumption constructed from thermal molecular agitation analogy. This formulation, emerging from uncertainties on the fluid parcels location, explains with another viewpoint some subgrid eddy diffusion models currently used in computational fluid dynamics or in geophysical sciences and paves the way for new large-scales flow modeling. We finally describe an applications of our formalism to the derivation of stochastic versions of the Shallow water equations or to the definition of reduced order dynamical systems. 相似文献
15.
New anisotropic covariance models and estimation of anisotropic parameters based on the covariance tensor identity 总被引：2，自引：0，他引：2
Many heterogeneous media and environmental processes are statistically anisotropic. In this paper we focus on range anisotropy,
that is, stochastic processes with variograms that have direction dependent correlation lengths and direction independent
sill. We distinguish between two classes of anisotropic covariance models: Class (A) models are reducible to isotropic after
rotation and rescaling operations. Class (B) models can be separated into a product of one-dimensional functions oriented
along the principal axes. We propose a new Class (A) model with multiscale properties that has applications in subsurface
hydrology. We also present a family of Class (B) models based on non-Euclidean distance metrics that are generated by superellipsoidal
functions. Next, we propose a new method for determining the orientation of the principal axes and the degree of anisotropy,
i.e., the ratio(s) of the correlation lengths. This information reduces the degrees of freedom of anisotropic variograms and
thus simplifies the estimation procedure. In particular, Class (A) models are reduced to isotropic and Class (B) models to
one-dimensional functions. Our method is based on an explicit relation between the second-rank slope tensor (SRST), which
can be estimated from the data, and the covariance tensor. The procedure is conceptually simple and numerically efficient.
It is more accurate for regular (on-grid) data distributions, but it can also be used for sparse (off-grid) spatial distributions.
In the case of non-differentiable random fields the method can be extended using generalized derivatives. We illustrate its
implementation with numerical simulations. 相似文献
16.
一种模拟随机数字地层模型的方法 总被引：2，自引：1，他引：1
介绍了一种利用计算机生成随机数字地层模型的方法。此方法根据给定的地层厚度及参数统计特性．按截尾正态分布进行随机抽样构建随机分层结构,并对各分层参数随机赋值,完成随机模型的构筑。用此方法可以很容易地在计算机上生成大量符合某种统计特性的随机数字层状地层模型,从而可以在这些模型上进行感兴趣的仿真模拟研究。为展示这一方法的应用,生成了10个第四系随机层状模型,并在这些模型上进行了地震SH波的地震动放大效应数字模拟实验。结果发现随机模型的响应无论在形态特点还是幅值上都与均值模型的响应显著不同,表明用不完全准确的参数模型模拟估计场址地震动响应时必须充分考虑到参数不准导致的误差。 相似文献
17.
The stochastic model has been widely used for the simulation study. However, there was a difficulty in the reproduction of the skewness of observed series and so the stochastic model for the skewness preservation was appeared. While the skewness in the residuals of the stochastic model has been considered for the skewness preservation this study uses a random resampling technique of residuals from the stochastic models for the simulation study and for the investigation of the skewness coefficient. The main advantage of this resampling scheme, called the bootstrap method is that it does not rely on the assumption of population distribution and this study uses the combined model of the stochastic and bootstrapped models. The stochastic and bootstrapped stochastic (or combined) models are used for the investigations of skewness preservation and of the reproduction of probability density function between the simulated series. The models are applied to the annual and monthly streamflows of Yongdam site in Korea and Yakima river, Washington, USA for the streamflow simulation study then the statistics and probability density functions for the observed and simulated streamflows are compared. As the results the bootstrapped stochastic model reproduces the skewness and probability density function much better than the stochastic model. This evidences suggest that the bootstrapped stochastic model might be more appropriate than the stochastic model for the preservation of skewness and for simulation purposes of the series. 相似文献
18.
AbstractBasic hidden Markov models are very useful in stochastic environmental research but their ability to accommodate sufficient dependence between observations is somewhat limited. However, they can be modified in several ways to form a rich class of flexible models that are useful in many environmental applications. We consider a class of hidden Markov models that incorporate additional dependence among observations to model average regional rainfall time series. The focus of the study is on models that introduce additional dependence between the state level and the observation level of the process and also on models that incorporate dependence at observation level. Construction of the likelihood function of the models is described along with the usual second-order properties of the process. The maximum likelihood method is used to estimate the parameters of the models. Application of the proposed class of models is illustrated in an analysis of daily regional average rainfall time series from southeast and southwest England for the winter season during 1931 to 2010. Models incorporating additional dependence between the state level and the observation level of the process captured the distributional properties of the daily rainfall well, while the models that incorporate dependence at the observation level showed their ability to reproduce the autocorrelation structure. Changes in some of the regional rainfall properties during the time period are also studied.Editor D. Koutsoyiannis 相似文献
19.
Hyun-Han Kwon Young-Il Moon 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,20(4):223-237
Hydrologic risk analysis for dam safety relies on a series of probabilistic analyses of rainfall-runoff and flow routing models, and their associated inputs. This is a complex problem in that the probability distributions of multiple independent and derived random variables need to be estimated in order to evaluate the probability of dam overtopping. Typically, parametric density estimation methods have been applied in this setting, and the exhaustive Monte Carlo simulation (MCS) of models is used to derive some of the distributions. Often, the distributions used to model some of the random variables are inappropriate relative to the expected behaviour of these variables, and as a result, simulations of the system can lead to unrealistic values of extreme rainfall or water surface levels and hence of the probability of dam overtopping. In this paper, three major innovations are introduced to address this situation. The first is the use of nonparametric probability density estimation methods for selected variables, the second is the use of Latin Hypercube sampling to improve the efficiency of MCS driven by the multiple random variables, and the third is the use of Bootstrap resampling to determine initial water surface level. An application to the Soyang Dam in South Korea illustrates how the traditional parametric approach can lead to potentially unrealistic estimates of dam safety, while the proposed approach provides rather reasonable estimates and an assessment of their sensitivity to key parameters. 相似文献
20.
Complexity 总被引：1，自引：0，他引：1
Gómez-Hernández JJ 《Ground water》2006,44(6):782-785
It is difficult to define complexity in modeling. Complexity is often associated with uncertainty since modeling uncertainty is an intrinsically difficult task. However, modeling uncertainty does not require, necessarily, complex models, in the sense of a model requiring an unmanageable number of degrees of freedom to characterize the aquifer. The relationship between complexity, uncertainty, heterogeneity, and stochastic modeling is not simple. Aquifer models should be able to quantify the uncertainty of their predictions, which can be done using stochastic models that produce heterogeneous realizations of aquifer parameters. This is the type of complexity addressed in this article. 相似文献